Novel fixed-time convergent multi-power reaching law
PU Ming
LIAO Jian-chun
DAN Zhi-hong
ZHANG Song
ZHANG Ge-xiang
LIU Peng
Abstract：Aiming at the shortcomings of the latest power sliding mode reaching law,such as weak adaptability,slow convergence speed of the whole domain and singularity at the initial point,a novel multi-power sliding mode reaching law considering both fixed-time convergence and finite-time convergence is proposed.Based on the existing power approach law,the approach law introduces a variable base function and a combination function combining power function and exponential function,which improves the adaptive ability and convergence speed of sliding mode in different approach stages,and satisfies the chattering free constraint.It is proved theoretically that the approach law in this paper is faster than the latest power approach law in the existing literature at every point in the state space except the origin,and the analytical expressions of the fixed-time upper bound of the convergence time and the steady-state error independent of the initial error are further derived.Finally,the simulation results show that the proposed scheme reduces the total errors of the three approach laws by about 74.7％,59.9％and 54.1％respectively under the condition of large disturbance and large initial error.When the state feedback signal is interfered with by 30 dB noise,the total error of the proposed scheme is reduced 73.4％,57.8％and 51.7％respectively compared with the three approach laws.These simulations have verified the superiority and effectiveness of the approach law in this paper.
Keywords：multi-power reaching lawsliding mode controlfixed timeconvergence ratesteady-state error bound
Publication Date：2025-05-30
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：12( 967-978 )